Question

A standard electric kettle uses 2000 Watts of electrical power. Power is defined as the energy transfer per unit time interval. Assuming that all the energy from the kettle is transferred to the water, determine how long a kettle should be switched on to bring 750 ml of water from standard room temperature to the boiling point,when Standard room temperature is 21° C and the boiling point of water is 99° C.

Answer 1

Solution.

$P=2000Watt;$

$V=750mL=0.75\sdot10^{-3}m^3;$

$t_1=21^oC;$

$t_2=99^oC;$

$\tau - ?$

$A=P\sdot\tau;$

$Q=cm\Delta t;$

$A=Q;$

$\tau=\dfrac{A}{P}=\dfrac{Q}{P};$

$c=4200J/(kg^oC);$

$m=\rho V;$

$\rho = 1000kg/m^3;$

$m=1000kg/m^3\sdot0.75\sdot 10^{-3}m^3=0.75kg;$

$Q=4200J/(kg^oC)\sdot0.75kg\sdot78^oC=245700J;$

$\tau=\dfrac{245700J}{2000Watts}=122.85s;$

Answer: $\tau = 122.85s.$